In this work, we introduce the Local SFGD
to estimate the low-rank factor of a density matrix over a set of local machines.
Although our main application is to solve the distributed QST objective in (REF ), Local SFGD can be more generally applied to the distributed SDP objective in (REF ); see Section  for details.
Local SFGD is summarized in Algorithm . While there are non-convex results on Local SGD [1]}, [2]}, they consider a different problem setting,
and only provide convergence in terms of the norm of the gradient.
To the best of our knowledge, this is the first work that studies Local SGD in the non-convex factorized objective, and
provides convergence in terms of the distance to the optimal model parameters.
